A034863 a(n) = n!*(4*n^3 - 30*n^2 + 40*n + 3)/24.

-61, -235, 810, 38850, 757680, 12836880, 212133600, 3554258400, 61372080000, 1100366467200, 20555914579200, 400638734496000, 8148554878464000, 172878910364160000, 3823017399032832000, 88035572875041792000, 2108819186504110080000

Offset

4,1

Links

G. C. Greubel, Table of n, a(n) for n = 4..445

J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.

Formula

Conjecture: (-96*n + 27161)*a(n) + (96*n^2 - 99580*n + 199917)*a(n-1) +(72707*n - 61983)*(n-1)*a(n-2) = 0. - R. J. Mathar, Apr 03 2017

E.g.f.: x^4*(-61 + 197*x - 151*x^2 + 39*x^3)/(24*(1-x)^4). - G. C. Greubel, Feb 16 2018

Maple

[seq(factorial(n)*(4*n^3-30*n^2+40*n+3)/24, n=4..22)]; # Muniru A Asiru, Feb 17 2018

Mathematica

Table[n!(4n^3-30n^2+40n+3)/24, {n, 4, 20}] (* Harvey P. Dale, Apr 14 2015 *)

Prog

(PARI) for(n=4, 30, print1(n!*(4*n^3-30*n^2+40*n+3)/24, ", ")) \\ G. C. Greubel, Feb 16 2018
(Magma) [Factorial(n)*(4*n^3-30*n^2+40*n+3)/24: n in [4..30]]; // G. C. Greubel, Feb 16 2018
(GAP) A034863:=List([4..22], n->Factorial(n)*(4*n^3-30*n^2+40*n+3)/24); # Muniru A Asiru, Feb 17 2018

Crossrefs

Sequence in context: A297731 A228130 A142267 * A251312 A158673 A174333

Adjacent sequences: A034860 A034861 A034862 * A034864 A034865 A034866

Keyword

sign

Author

N. J. A. Sloane

Extensions

More terms from Harvey P. Dale, Apr 14 2015

Status

approved